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Number of 3Xn 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero
1

%I #4 Nov 06 2013 18:32:27

%S 0,0,8,76,834,9488,105962,1179364,13125298,146097624,1626238194,

%T 18101813556,201493039018,2242839951880,24965287273578,

%U 277891238282180,3093236609372642,34431142194463224,383256667023706306

%N Number of 3Xn 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero

%C Row 3 of A231285

%H R. H. Hardin, <a href="/A231286/b231286.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 26*a(n-1) -267*a(n-2) +1560*a(n-3) -6087*a(n-4) +17438*a(n-5) -38845*a(n-6) +70000*a(n-7) -108952*a(n-8) +161144*a(n-9) -214028*a(n-10) +150344*a(n-11) +187284*a(n-12) -587360*a(n-13) +482160*a(n-14) +11936*a(n-15) -126224*a(n-16) -26496*a(n-17) -29888*a(n-18) +19968*a(n-19) for n>21

%e Some solutions for n=3

%e ..0..1..2....0..1..2....0..1..2....0..1..2....0..1..0....0..1..0....0..1..2

%e ..0..3..0....0..3..2....2..3..0....0..3..2....2..3..0....2..3..2....2..3..2

%e ..2..1..0....2..1..0....2..1..0....0..1..0....2..1..0....0..1..0....0..1..0

%K nonn

%O 1,3

%A _R. H. Hardin_, Nov 06 2013